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Factorize the polynomial expression $x^{2} - 4 x - 12$ , and choose the correct option which represents the factored form correctly.

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(x + 4) (x + 3)

(x + 6) (x - 2)

(x - 6) (x + 2)

(x + 2) (x - 1)

answer is C.

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Detailed Solution

The given expression is as follows,

x^{2} - 4 x - 12

.
So, to proceed with the factorization, we first need to take the product of the first and last terms of the above expression, i.e.,

x^{2} \times (- 12) = - 12 x^{2}

Next, we need to split middle term of the polynomial expression, i.e.,

- 4 x

as a sum or difference of two terms, such that their product is equal to the product of first and last terms, i.e.,

- 12 x^{2}

x^{2} - 4 x - 12 \Leftrightarrow x^{2} - 6 x + 2 x - 12

Now, we need to group the terms and factor out the common factors, as follows,

\begin{matrix} (x^{2} - 6 x) + (2 x - 12) = x (x - 6) + 2 (x - 6) \\ = (x - 6) (x + 2) \end{matrix}

So, the factored form of the given polynomial expression is

(x - 6) (x + 2)

.
Hence, the correct option is (3).

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